Added some tests for trig functions in Math module. Also, tests are made...

Added some tests for trig functions in Math module. Also, tests are made against a tolerance on Floats

test/t/math.rb

 ##
 # Math Test
 
+MATH_TOLERANCE = 1E-12
+def check(a,b)
+  a = a.to_f
+  b = b.to_f
+  if a.finite? and b.finite?
+    (a-b).abs < MATH_TOLERANCE
+  else
+    true
+  end
+end
+
+
+assert('Math.sin 0') do
+  check(Math.sin(0), 0)
+end
+
+assert('Math.sin PI/2') do
+  check(Math.sin(Math::PI / 2), 1)
+end
+
+
+assert('Fundamental trig identities') do  
+  result = true
+  N = 15
+  N.times do |i|
+    a = Math::PI / N * i
+    s = Math.sin(a)
+    c = Math.cos(a)
+    t = Math.tan(a)
+    result &= check(s, Math.cos(Math::PI / 2 - a))
+    result &= check(t, 1 / Math.tan(Math::PI / 2 - a))
+    result &= check(s ** 2 + c ** 2, 1)
+    result &= check(t ** 2 + 1, (1/c) ** 2)
+    result &= check((1/t) ** 2 + 1, (1/s) ** 2)
+  end
+  result
+end  
+
 assert('Math.erf 0') do
-  Math.erf(0) == 0
+  check(Math.erf(0), 0)
 end
 
 assert('Math.exp 0') do
-  Math.exp(0) == 1.0
+  check(Math.exp(0), 1.0)
 end
 
 assert('Math.exp 1') do
-  Math.exp(1) == 2.718281828459045
+  check(Math.exp(1), 2.718281828459045)
 end
 
 assert('Math.exp 1.5') do
-  Math.exp(1.5) == 4.4816890703380645
+  check(Math.exp(1.5), 4.4816890703380645)
 end
 
 assert('Math.log 1') do
-  Math.log(1) == 0
+  check(Math.log(1), 0)
 end
 
 assert('Math.log E') do
-  Math.log(Math::E) == 1.0
+  check(Math.log(Math::E), 1.0)
 end
 
 assert('Math.log E**3') do
-  Math.log(Math::E**3) == 3.0
+  check(Math.log(Math::E**3), 3.0)
 end
 
 assert('Math.log2 1') do
-  Math.log2(1) == 0.0
+  check(Math.log2(1), 0.0)
 end
 
 assert('Math.log2 2') do
-  Math.log2(2) == 1.0
+  check(Math.log2(2), 1.0)
 end
 
 assert('Math.log10 1') do
-  Math.log10(1) == 0.0
+  check(Math.log10(1), 0.0)
 end
 
 assert('Math.log10 10') do
-  Math.log10(10) == 1.0
+  check(Math.log10(10), 1.0)
 end
 
 assert('Math.log10 10**100') do
-  Math.log10(10**100) == 100.0
+  check(Math.log10(10**100), 100.0)
 end
 
 assert('Math.cbrt') do
-  a = [-8, -1, 0, 1, 8].map do |i|
-    Math.cbrt(i)
+  num = [-2.0, -1.0, 0.0, 1.0, 2.0]
+  cub = [-8, -1, 0, 1, 8]
+  result = true
+  cub.each_with_index do |v,i|
+    result &= check(Math.cbrt(v), num[i])
   end
-
-  a == [-2.0, -1.0, 0.0, 1.0, 2.0]
+  result
 end
 
 assert('Math.hypot') do
-  Math.hypot(3, 4) == 5.0
+  check(Math.hypot(3, 4), 5.0)
 end